ECON 3209 · Week 19, Lecture 2 · Kerala Agricultural University
Department of Development Economics, KAU
Autumn 2026
Learning Outcomes
By the end of this lecture, you should be able to:
define a unit root and relate it to random-walk behaviour
run and interpret the Augmented Dickey-Fuller test
compare ADF and KPSS hypotheses
test level and differenced series in Python
apply these ideas to Kerala paddy production data
What Is a Unit Root?
A simple random walk is:
\[Y_t = Y_{t-1} + \varepsilon_t\]
Shocks have permanent effects.
The series wanders without returning to a fixed mean.
This is the classic nonstationary unit-root case.
ADF Test Logic
The Augmented Dickey-Fuller test estimates a regression with lagged levels and lagged differences.
Null hypothesis: the series has a unit root (nonstationary).
Alternative: the series is stationary.
A small p-value leads us to reject the unit-root null.
KPSS Complements ADF
ADF null: unit root.
KPSS null: stationarity.
Because the nulls differ, the two tests complement each other.
Together they provide a more balanced diagnosis.
Simulating a Stationary Series and a Random Walk
ADF and KPSS in Python
Reading the Tests
ADF small p-value → evidence against a unit root.
KPSS small p-value → evidence against stationarity.
Strongest conclusion comes when the two tests agree.
If they disagree, inspect plots, sample size, lag choice, and economic context.
Kerala Paddy Series
Visualising Level and First Difference
Decision Grid
ADF result
KPSS result
Typical interpretation
Reject unit root
Fail to reject stationarity
Stationary
Fail to reject unit root
Reject stationarity
Nonstationary
Both reject
Possible structural break / ambiguity
Both fail to reject
Low power / inconclusive
Always combine tests with economic reasoning.
Why It Matters for Forecasting
ARIMA models require correct differencing.
If we ignore unit roots, forecasts may be unstable and inference misleading.
Proper testing helps choose whether the integration order \(d\) should be 0, 1, or higher.
Exercise
Run ADF and KPSS on the paddy series in levels and first differences. Which version looks more stationary, and what does that imply for ARIMA differencing?
Summary
✅ A unit root implies shocks have persistent effects and the series is usually nonstationary in levels.
✅ ADF tests the null of a unit root, while KPSS tests the null of stationarity.
✅ Testing both levels and first differences helps determine the amount of differencing needed.
✅ This decision is central for building ARIMA models in the next week.
Next Lecture
We use ACF and PACF plots to identify AR and MA structure.
You will learn how lag patterns guide order selection.
This is the bridge from stationarity testing to ARIMA design.